Recall that each proposal has a (latent) binary label \(\mathbf {z}_{ij} \in \lbrace 0, 1\rbrace \)  that indicates whether the proposal
tightly encloses the common object. Following the best practice of the
previous works in WSOD [1]}, [2]}, [3]}, we assume there is exactly one
proposal with label 1 (positive proposal) in each image and the rest are
negative proposals, i.e., \(\mathbf {z}_i \in \lbrace \mathbf {e}_1, \dots \mathbf {e}_P\rbrace \)  where
\(\mathbf {e}_j\in \lbrace 0,1\rbrace ^P\)  is the \(j\) -th canonical basis.
